New posts in Nonstandard Models

Why do models of ZF which are not $\omega$-models have non-standard formulas whose length is "infinitely large natural numbers"?

Can proper elementarily equivalent end extensions ever be definable?

Relationship between nonstandard analysis and nonstandard models of arithmetic

Can additional predicates "eliminate" nonstandard models of true arithmetic?

What is an example of a non standard model of Peano Arithmetic?

How does induction fail in computable nonstandard models?

Prime numbers on a non-standard model