Study mathematical logic and set theory
121
Sub Topics
271
MCQs
92
MCOs
194
True/False
107
Fill Blanks
29
Rearrange
94
Matching
40
Comprehensions
84
Flashcard Decks
Curriculum
What You'll Learn
01 Introduction to Logic 3 topics
1 Historical Development of Logic
- Ancient Logic (Aristotle, Stoics)
- Medieval Logic
- Modern Logic (Frege, Russell, Gödel)
2 Logical Reasoning and Argument
- Deductive vs. Inductive Reasoning
- Validity and Soundness
- Logical Fallacies
3 The Language of Logic
- Statements and Propositions
- Truth Values
- Logical Form
02 Propositional Logic 4 topics
1 Syntax of Propositional Logic
- Atomic and Compound Propositions
- Logical Connectives
- Well-Formed Formulas
2 Semantics of Propositional Logic
- Truth Tables
- Tautologies, Contradictions, and Contingencies
- Logical Equivalence
3 Normal Forms
- Conjunctive Normal Form (CNF)
- Disjunctive Normal Form (DNF)
4 Formal Deduction in Propositional Logic
- Rules of Inference
- Natural Deduction
- Axiomatic Systems
03 Predicate Logic 4 topics
1 First-Order Logic
- Syntax (Terms, Predicates, Quantifiers)
- Variables and Constants
- Free and Bound Variables
2 Semantics of Predicate Logic
- Interpretations and Models
- Satisfaction and Truth
- Validity in Predicate Logic
3 Formal Deduction in Predicate Logic
- Rules for Quantifiers
- Universal and Existential Instantiation
- Universal and Existential Generalization
4 Limitations of First-Order Logic
- Higher-Order Logic
- Non-Classical Logics
04 Set Theory Fundamentals 4 topics
1 Basic Concepts
- Sets and Elements
- Set Notation and Representation
- Empty Set and Universal Set
2 Set Operations
- Union and Intersection
- Complement and Difference
- Cartesian Product
3 Set Relations
- Subset and Proper Subset
- Set Equality
- Power Sets
4 Families of Sets
- Indexed Families
- Algebras of Sets
- Boolean Algebras
05 Relations and Functions 4 topics
1 Binary Relations
- Definition and Properties
- Reflexivity, Symmetry, Transitivity
- Equivalence Relations and Partitions
2 Ordering Relations
- Partial Orders
- Total Orders
- Well-Orders
3 Functions
- Definition and Properties
- Injective, Surjective, and Bijective Functions
- Composition of Functions
- Inverse Functions
4 Special Functions
- Identity Function
- Characteristic Functions
- Choice Functions
06 Cardinality 4 topics
1 Finite and Infinite Sets
- Counting Principles
- Pigeonhole Principle
2 Countable Sets
- Denumerable Sets
- Properties of Countable Sets
3 Uncountable Sets
- Cantor's Diagonal Argument
- The Continuum
4 Cardinal Numbers
- Definition and Ordering
- Cardinal Arithmetic
- Continuum Hypothesis
07 Axiomatic Set Theory 4 topics
1 Paradoxes in Naive Set Theory
- Russell's Paradox
- Burali-Forti Paradox
- Cantor's Paradox
2 Zermelo-Fraenkel Set Theory
- Axiom of Extensionality
- Axiom of Pairing
- Axiom of Union
- Axiom of Power Set
- Axiom Schema of Separation
- Axiom Schema of Replacement
- Axiom of Infinity
- Axiom of Foundation
3 The Axiom of Choice
- Equivalent Formulations
- Zorn's Lemma
- Well-Ordering Principle
4 Alternative Axiomatic Systems
- Von Neumann–Bernays–Gödel Set Theory
- New Foundations
08 Ordinal Numbers 4 topics
1 Well-Ordered Sets
- Properties and Examples
- Ordinal Numbers as Order Types
2 Ordinal Arithmetic
- Addition
- Multiplication
- Exponentiation
3 Transfinite Recursion
- Definition by Transfinite Recursion
- Transfinite Induction
4 Ordinal Hierarchies
- Successor and Limit Ordinals
- Countable Ordinals
- Uncountable Ordinals
09 Models of Set Theory 4 topics
1 Constructible Universe
- Gödel's L
- Constructible Hierarchy
2 Forcing
- Cohen's Method
- Generic Extensions
3 Large Cardinals
- Inaccessible Cardinals
- Measurable Cardinals
- Supercompact Cardinals
4 Inner Models
- Core Models
- Fine Structure Theory
10 Applications and Advanced Topics 4 topics
1 Logic in Computer Science
- Formal Verification
- Logic Programming
- Automated Theorem Proving
2 Set-Theoretic Topology
- Topological Spaces
- Continuity and Compactness
- Connectedness
3 Descriptive Set Theory
- Polish Spaces
- Borel and Analytic Sets
- Determinacy
4 Foundations of Mathematics
- Incompleteness Theorems
- Independence Results
- Alternative Foundations
11 Appendices 3 topics
1 Mathematical Induction
- Principle of Mathematical Induction
- Strong Induction
- Structural Induction
2 Formal Systems
- Syntax and Semantics
- Completeness and Soundness
- Decidability and Undecidability
3 Historical Notes and Biographies
- Key Figures in Logic
- Development of Set Theory
- Modern Developments
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Logic and Set Theory
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