A trichotomous relation means for any two objects, they are either related in one direction, the other direction, or are…
Transitivity is a fundamental property of relations. If A relates to B, and B relates to C, then A must…
Topos theory studies categories resembling the category of sets, forming a foundation for mathematics. It enables generalized concepts of computation…
Topos theory generalizes set theory using abstract frameworks. It defines mathematical structures across various contexts, offering a powerful lens for…
Symmetry in binary relations means if A is related to B, then B is also related to A. It's a…
A surjection, or onto function, ensures every element in the target set is reached by at least one element from…
The successor function, denoted S(n) = n + 1, is a foundational concept in arithmetic and logic, defining the next…
A relation R is strongly connected if for any two elements x and y, either x is related to y…
The Skolem paradox highlights a contradiction between intuition and the Skolem-Lowenheim theorem. It shows that countable models can exist for…
A fundamental theorem in first-order logic. It asserts that if a theory has an infinite model, it possesses models for…