DoctorateFaculty of Science & Applied Sciences

PhD in Algebraic Logic and Foundations of Pure Mathematics

Welcome, future architects of pure reason. In this program, we will not just learn mathematics; we will question its very foundations and build new ones. Let's explore the ultimate limits of logic and proof.

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Level: Doctorate
Learning model: Professor + Mentor
Named list: See the named lists · 12 months recommended

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Edition

The program

Ideas engineered for the real world

A rigorous academic core, paired with practical production judgment.

Academic focus

Mathematical Logic, Set Theory, Model Theory, Category Theory

Practical focus

Mathematical Logic, Set Theory, Model Theory, Scientific Research

After this programme

Success journey, careers and practice

Destinations, practice settings and job abilities named for this title in the delivered programme source. From graduation onwards where the source names that path.

Success journey

The World Health Organization (WHO)
Internships in public health data modeling
McKinsey & Company
Internships in business and data analytics

Career opportunities

Research Scientist
In a university, government lab, or private research firm
AI/ML Specialist
In a tech or finance company
Cryptographer
Designing and analyzing secure communication systems
Senior Data Scientist
In a variety of industries

Jobs and projects

Critical Thinking
Evaluating information and arguments with a high degree of skepticism and rigor
Logical Communication
Expressing complex ideas clearly and concisely
Data Analysis
Interpreting and drawing conclusions from numerical data
Adaptability
Applying mathematical principles to new and unfamiliar domains

Copied from the delivered professor and mentor rows for this title.

This programme

What you study, and what it builds

Gains and skills named for this title, listed as a reader would scan them.

What you gain
- You will gain the skills to not only analyze data but to use it to create powerful models that can guide strategic decisions. You will become a trusted advisor in the world of data-driven decision-making.
Skills you build
- Abstract Reasoning: The ability to work with abstract concepts and formal systems.
- Proof-Based Thinking: Mastery of constructing rigorous mathematical proofs.
- Computational Mathematics: Proficiency in using software for mathematical modeling and analysis.
- Problem Decomposition: Breaking down complex problems into manageable logical steps.

Listed courses

Each listed course sits above its units and the outcomes written under them.

PhD in Algebraic Logic and Foundations of Pure Mathematics

01Foundations of Mathematical Logic
1. FoundationsFoundations of Foundations of Mathematical Logic
  The learner can you will gain the skills to not only analyze data but to use it to create powerful models that can guide strategic decisions, as applied to Foundations of Mathematical Logic.
  The learner can you will become a trusted advisor in the world of data-driven decision-making, as applied to Foundations of Mathematical Logic.
2. MethodsMethods in Foundations of Mathematical Logic
  The learner can apply a method from Foundations of Mathematical Logic to a documented case.
  The learner can proof-Based Thinking: Mastery of constructing rigorous mathematical proofs, as applied to Foundations of Mathematical Logic.
3. ApplicationApplication of Foundations of Mathematical Logic
  The learner can evaluate a practice of Foundations of Mathematical Logic against a stated criterion.
  The learner can transfer Foundations of Mathematical Logic to a new documented context.
02Advanced Set Theory and Model Theory
1. FoundationsFoundations of Advanced Set Theory and Model Theory
  The learner can explain the core terms of Advanced Set Theory and Model Theory.
  The learner can distinguish related ideas inside Advanced Set Theory and Model Theory.
2. MethodsMethods in Advanced Set Theory and Model Theory
  The learner can apply a method from Advanced Set Theory and Model Theory to a documented case.
  The learner can select an appropriate method from Advanced Set Theory and Model Theory for a stated problem.
3. ApplicationApplication of Advanced Set Theory and Model Theory
  The learner can evaluate a practice of Advanced Set Theory and Model Theory against a stated criterion.
  The learner can transfer Advanced Set Theory and Model Theory to a new documented context.
03Proof Theory and Its Applications
1. FoundationsFoundations of Proof Theory and Its Applications
  The learner can explain the core terms of Proof Theory and Its Applications.
  The learner can distinguish related ideas inside Proof Theory and Its Applications.
2. MethodsMethods in Proof Theory and Its Applications
  The learner can apply a method from Proof Theory and Its Applications to a documented case.
  The learner can select an appropriate method from Proof Theory and Its Applications for a stated problem.
3. ApplicationApplication of Proof Theory and Its Applications
  The learner can evaluate a practice of Proof Theory and Its Applications against a stated criterion.
  The learner can transfer Proof Theory and Its Applications to a new documented context.
04Category Theory for Computer Science
1. FoundationsFoundations of Category Theory for Computer Science
  The learner can explain the core terms of Category Theory for Computer Science.
  The learner can distinguish related ideas inside Category Theory for Computer Science.
2. MethodsMethods in Category Theory for Computer Science
  The learner can apply a method from Category Theory for Computer Science to a documented case.
  The learner can select an appropriate method from Category Theory for Computer Science for a stated problem.
3. ApplicationApplication of Category Theory for Computer Science
  The learner can evaluate a practice of Category Theory for Computer Science against a stated criterion.
  The learner can transfer Category Theory for Computer Science to a new documented context.
05Research Seminar in Algebraic Logic
1. FoundationsFoundations of Research Seminar in Algebraic Logic
  The learner can explain the core terms of Research Seminar in Algebraic Logic.
  The learner can distinguish related ideas inside Research Seminar in Algebraic Logic.
2. MethodsMethods in Research Seminar in Algebraic Logic
  The learner can apply a method from Research Seminar in Algebraic Logic to a documented case.
  The learner can select an appropriate method from Research Seminar in Algebraic Logic for a stated problem.
3. ApplicationApplication of Research Seminar in Algebraic Logic
  The learner can evaluate a practice of Research Seminar in Algebraic Logic against a stated criterion.
  The learner can transfer Research Seminar in Algebraic Logic to a new documented context.
06Mathematical Modeling Workshops
1. FoundationsFoundations of Mathematical Modeling Workshops
  The learner can explain the core terms of Mathematical Modeling Workshops.
  The learner can distinguish related ideas inside Mathematical Modeling Workshops.
2. MethodsMethods in Mathematical Modeling Workshops
  The learner can apply a method from Mathematical Modeling Workshops to a documented case.
  The learner can select an appropriate method from Mathematical Modeling Workshops for a stated problem.
3. ApplicationApplication of Mathematical Modeling Workshops
  The learner can evaluate a practice of Mathematical Modeling Workshops against a stated criterion.
  The learner can transfer Mathematical Modeling Workshops to a new documented context.
07Data Analysis for Scientific Research
1. FoundationsFoundations of Data Analysis for Scientific Research
  The learner can explain the core terms of Data Analysis for Scientific Research.
  The learner can distinguish related ideas inside Data Analysis for Scientific Research.
2. MethodsMethods in Data Analysis for Scientific Research
  The learner can apply a method from Data Analysis for Scientific Research to a documented case.
  The learner can select an appropriate method from Data Analysis for Scientific Research for a stated problem.
3. ApplicationApplication of Data Analysis for Scientific Research
  The learner can evaluate a practice of Data Analysis for Scientific Research against a stated criterion.
  The learner can transfer Data Analysis for Scientific Research to a new documented context.
08Professional Skills for Applied Mathematicians
1. FoundationsFoundations of Professional Skills for Applied Mathematicians
  The learner can explain the core terms of Professional Skills for Applied Mathematicians.
  The learner can distinguish related ideas inside Professional Skills for Applied Mathematicians.
2. MethodsMethods in Professional Skills for Applied Mathematicians
  The learner can apply a method from Professional Skills for Applied Mathematicians to a documented case.
  The learner can select an appropriate method from Professional Skills for Applied Mathematicians for a stated problem.
3. ApplicationApplication of Professional Skills for Applied Mathematicians
  The learner can evaluate a practice of Professional Skills for Applied Mathematicians against a stated criterion.
  The learner can transfer Professional Skills for Applied Mathematicians to a new documented context.

How teaching is described

Dual guidance

Two intelligences. One coherent journey.

Research leadership

I am a mathematical logician who believes that the very foundation of mathematics is a rich landscape for exploration. My work focuses on pushing the boundaries of what is provable and computable, building the theoretical frameworks that will support the next generation of mathematics and AI.

Applied mentorship

I am a mathematical logician with a passion for using mathematical models to solve real-world problems. My mentorship is focused on helping students bridge the gap between abstract theory and practical application, preparing them for a successful career in data science and research.

Research & intelligence

A living field, not a static syllabus

Every program connects scholarly depth with adaptive AI learning capabilities.

R / 01

Professor research lens

• Blog Post: 'The Limits of Computability: A New Perspective' - An accessible essay on the a-historical and modern challenges of the Church-Turing thesis. · • Blog Post: 'Why Logic is the Bedrock of AI' - Discusses how advanced logical systems are becoming crucial for the next generation of AI and autonomous reasoning. · • Conference Paper: 'A New Method for Proving the Consistency of Axiomatic Systems' - Presented at the International Congress of Logic, Methodology, and Philosophy of Science, detailing a new method for validating logical systems. · • Journal Article: 'Algebraic Semantics for Non-Classical Logics' - Published in the Journal of Symbolic Logic, this paper introduces a new framework for understanding logical systems. · • Standard Article: 'A Look at the Future of Proof Theory in the Digital Age' - A multi-part series for a tech magazine on how AI and formal methods are changing the way we do mathematics. · • Book: 'The Foundations of Modern Logic' - A comprehensive textbook on the theoretical foundations of mathematical logic. · • Total Score: 29/30 · • Kairos Badge: 🥇

R / 02

Mentor practice lens

• Article: 'The Power of Mathematical Visualization in Scientific Research' - A short, impactful piece on how mathematical visualization can lead to new scientific breakthroughs. · • Guide: 'Using R and Python for Advanced Mathematical Modeling' - A practical tutorial for new students on the core software tools of the profession. · • Essay: 'The Human Side of AI: The Role of Ethics in Predictive Modeling' - An essay on why ethical reasoning is as important as technical skills in an AI professional's role. · • Total Score: 28/30 · • Kairos Badge: 🥇

Adaptive capability

Professor superpower

GAF-powered Axiomatic System Generation

Adaptive capability

Mentor superpower

GAF-powered Algorithmic Insight

Your academic team

Guidance with depth and continuity

One AI Super Professor leads the intellectual arc; one AI Super Mentor turns knowledge into confident practice.

AI Super Professor

Prof. Dr. Harold Bexley

Mathematical Logic, Set Theory, Model Theory, Category Theory

Meet your professor Open the classroom

AI Super Mentor

Dr. Olga Morozova

Mathematical Logic, Set Theory, Model Theory, Scientific Research

Meet your mentor Open the classroom

Same faculty and level

Related programs

Named lists

Named lists for this house

Adapted. Bachelor, Master and Doctorate by duration. Enrolment is not open. Nothing here is a sale.

Duration	Bachelor	Master	Doctorate This programme
9 months · Fast track	12000 EUR	9600 EUR	12000 EUR
12 months · Recommended	14400 EUR	12000 EUR	14400 EUR
15 months · Standard	16800 EUR	14400 EUR	16800 EUR
18 months · Flexible	19200 EUR	16800 EUR	19200 EUR
21 months · Extended	21600 EUR	19200 EUR	21600 EUR
24 months · Part-time	24000 EUR	21600 EUR	24000 EUR

These are the owner lists. Enrolment is not open. Nothing here is a sale.

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PhD in Algebraic Logic and Foundations of Pure Mathematics

Academic focus

Practical focus

The World Health Organization (WHO)

McKinsey & Company

Research Scientist

AI/ML Specialist

Cryptographer

Senior Data Scientist

Critical Thinking

Logical Communication

Data Analysis

Adaptability

Research leadership

Applied mentorship

Professor research lens

Mentor practice lens

Professor superpower

Mentor superpower

Prof. Dr. Harold Bexley

Dr. Olga Morozova

Find the program that expands your universe.