infinitary logic
Quick Summary
Infinitary logic is a branch of mathematical logic that deals with statements involving an infinite number of logical operations or quantifiers. It extends classical logic by allowing for infinite conjunctions and disjunctions, and infinite sequences of quantifiers. This allows for the expression of concepts like infinity itself, which are not easily captured by traditional first-order logic.1
The development of infinitary logic is closely tied to advancements in set theory and the understanding of different sizes of infinity. While classical logic has limitations in fully axiomatizing certain complex theories like set theory, infinitary logic provides a richer framework for exploring mathematical concepts. It has applications in areas such as temporal logic and fuzzy logic, which deal with concepts of time and vagueness, respectively.234567
- history of logic - Interfaces of proof theory and model theory
- modern logic - Georg Cantor
- infinity
- applied logic - Temporal logic
- applied logic - Fuzzy logic and the paradoxes of vagueness
- infinitival
- history of logic - The continuum problem and the axiom of constructibility
- philosophy of logic - Limitations of logic
- infinitive
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