 Infinitary logic

Infinitary logic permits infinitary syntactic operations, such as infinite conjunctions, together with an interpretation of its formulas. The infinitary language $L_{\kappa ,\lambda }$ specifies the permitted conjunction and quantifier lengths.

Infinitary logic is an extension of classical logic that allows for formulas to have infinite lengths, enabling the expression of more complex properties of mathematical structures. Unlike standard first-order or second-order logics, where formulas are made up of a finite number of symbols, infinitary logic permits formulas with infinitely many variables or connectives.