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Forcing (mathematics) Boolean-valued model; Kripke semantics. General frame; Predicate logic. First-order logic. Infinitary logic; Many-sorted logic; Higher-order logic. Lindström quantifier; Second-order logic; Soundness theorem; Gödel's completeness theorem. Original proof of Gödel's completeness theorem; Compactness theorem; Löwenheim ...
Mathematical logic is the study of formal logic within mathematics. Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power. Mathematical logic is divided into four parts: Model theory; Proof theory; Recursion theory, also known as computability theory ...
Categorical logic is the branch of mathematics in which tools and concepts from category theory are applied to the study of mathematical logic. It is also notable for its connections to theoretical computer science. [1] In broad terms, categorical logic represents both syntax and semantics by a category, and an interpretation by a functor.
Venn diagrams are illustrations of set theoretical, mathematical or logical relationships. Logic is the foundation that underlies mathematical logic and the rest of mathematics. It tries to formalize valid reasoning. In particular, it attempts to define what constitutes a proof. List of Boolean algebra topics
Combinatorics – the branch of mathematics concerning the study of finite or countable discrete structures. Geometry – this is one of the oldest branches of mathematics, it is concerned with questions of shape, size, relative position of figures, and the properties of space. Algebraic geometry – study of zeros of multivariate polynomials.
Logic is the formal science of using reason and is considered a branch of both philosophy and mathematics and to a lesser extent computer science. Logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and the study of arguments in natural language .
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