Questions tagged [axioms]
An axiom is a proposition in logic that a given theory requires to be true: every model of the theory is required to make the axiom hold true. The sense however is that an axiom is a basic true proposition, used to prove other true propositions (the theorems) in the theory. (from nLab).
2
questions
3
votes
2
answers
118
views
Is the validity of induction in Coq axiomatic?
When one defines an inductive type in Coq, for example, natural numbers,
Inductive nat : Set :=
| O : nat
| S : nat -> nat.
Coq automatically creates an ...
- 33
2
votes
2
answers
206
views
What is known about minimal sets of axioms? [closed]
There are several axioms that are known to be independent of the usual ones; for instance, the Axiom of Choice. This axiom can be stated in several equivalent ways, e.g.:
For every set $A$, $\mathcal{...
- 495