# Tagged Questions

**6**

votes

**5**answers

769 views

### Formal proof of Con(ZFC) => Con(ZFC + not CH) in ZFC

Is it possible to prove $Con(ZFC) \rightarrow Con(ZFC + \neg CH)$ purely within ZFC? To prove this (using forcing) one seems to need a countable transitive model of ZFC. The texts I am reading avoid ...

**10**

votes

**3**answers

623 views

### Complete Extensions of First Order Logic (or Language)

Lindstrom's theorem states that any extension of FOL more expressible than FOL fails to have either compactness or Lowenheim-Skolem. When I first read Lindstrom's theorem my first reaction was: "Does ...

**5**

votes

**2**answers

581 views

### Are computable models sufficient?

What I mean is this. By downward Lowenheim-Skolem theorem, first-order formula Q is a always true iff it is true in every countable structure. But is there some first-order formula Q which is true in ...

**2**

votes

**3**answers

469 views

### Given is “model”. How many theories may it be a model?

Usually we have axiomatic theory and the we look for model for it - this is book picture. Of course in real math usual one has a "model" that is given structure and looks for proper axiomatizing of ...

**1**

vote

**0**answers

206 views

### Classification of properties of structures

Is there a sensible classification of the properties of structures with a given signature $\sigma$, e.g. graphs with $\sigma = \lbrace R \rbrace$?
For example like this:
properties defined by ...

**6**

votes

**3**answers

487 views

### What assumptions and methodology do metaproofs of logic theorems use and employ?

In logic modules, theorems like Soundness and completeness of first order logic are proved. Later, Godel's incompleteness theorem is proved. May I ask what are assumed at the metalevel to prove such ...