# Tagged Questions

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### set theory, Incompleteness and axiomatic systems

Is the number of theorems that can be proved (decidable) within a certain set of axioms (for instance ZFC) is finite or infinite ? in other words, are we going to fully exhaust that set of axioms ...
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### How to deal with equivalences in proofs?

There is a part I need clarification on regarding the use of equivalence and its symmetry. From what I understand in regards to symmetry is that: $(p \equiv q) \equiv (q \equiv p)$. Given p and q ...
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### Does every mathematical principle have a proof?

My question actually narrows down to the meaning of mathematical principle. While I'm looking for some principles, they usually have their proofs, so I thought "principle" has the same meaning as ...
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### Can a set of theorem be derived from different sets of incompatible axioms? [closed]

Let's take T = {set of statements} that can be derived from S1 = {set of axiom}. Assuming that we keep the same derivation rules, are there any other S, with S1 & S always false, from which we can ...
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### Set of true statements generated by set of axioms with a binary operator

I wondered about this and I am having a hard time formulating it as a question at all, but I hope I can express something if my wondering here. Assume we have a set $V = \{\mathbb N, +, =, X ,(,)\}$. ...
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