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Questions tagged [set-theory]

Set theory is the branch of mathematics that studies unordered collections of objects. Questions with this tag will involve proofs about sets or operations on them.

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16 votes
3 answers
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Do you need a Hilbert style Epsilon operator for definitions in set theory?

I've started to play with mechanizing some set theory stuff. I'm not sure if I want a constructive flavor or not yet. Anyhow you can do stuff like axiomize the empty set $$ \top \vdash \exists P. \...
Ms. Molly Stewart-Gallus's user avatar
26 votes
2 answers
1k views

What set-theoretic definitions can't easily be formalized in a type theory?

Most proof assistants (with some exceptions like Isabelle/ZF or the B method) rely on type theory. See also the MathOverflow question What makes dependent type theory more suitable than set theory for ...
ErikMD's user avatar
  • 406
14 votes
4 answers
1k views

Open source proof assistants for first order logic with equality and set theory

I have been trying to find open source proof assistants for first order logic with equality and set theory. To date, the closest that I have found is Metamath (http://us.metamath.org/index.html) and ...
user695931's user avatar
7 votes
2 answers
1k views

Is it possible to make a proof assistant program based on ZFC?

I heard that many proof assistant programs are made based on the type theory. For me, as a mathematician, when I met Coq at first, it is difficult to accustomed with it. So I have a question. Is it ...
with-forest's user avatar
4 votes
2 answers
411 views

Is there a "standard" encoding or model of material set theory in type theory?

I am a little aware of various attempts to axiomize set theory within a theorem prover. Is there a standard kind of encoding of sets? An organic model to interpret set theories into? I would like to ...
Ms. Molly Stewart-Gallus's user avatar