Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Possible Duplicate:
What are the consequences if Axiom of Infinity is negated?

In ZFC, if we replace Ax.Inf to such a statement that every set is finite, then does this theory satisfiable?

share|cite|improve this question

marked as duplicate by Asaf Karagila, rschwieb, Chris Eagle, Ross Millikan, Thomas Oct 20 '12 at 14:47

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

up vote 3 down vote accepted

Yes: $V_\omega$, the set of hereditarily finite sets, is a model of $(\mathrm{ZFC}-\mathrm{Inf})+\lnot\mathrm{Inf}$.

share|cite|improve this answer
You mean of course (ZFC-Inf)$+\neg$ Inf. – Hagen von Eitzen Oct 20 '12 at 13:02
@Hagen: I do indeed; thanks. – Brian M. Scott Oct 20 '12 at 13:03

Not the answer you're looking for? Browse other questions tagged or ask your own question.