# Tag Info

Accepted

### Terminology question regarding $L$ and "definable" real numbers

The two collections in question are a priori extremely different. (To avoid metamathematical issues which obscure the subject in my opinion, I'm going to focus on the situation relative to a model in ...
• 249k

### How create truth table for ZFC axioms. What type of variables will be in the cells of this table?

Truth-tables are completely inappropriate for this. Truth-tables are used in propositional logic, sometimes called sentential logic or truth-functional logic, which analyzes statements at the 'level' ...
• 101k
1 vote
Accepted

### Demonstration of the inverse additive of an element of Z is unique

If you are working in a structure that assumes commutativity as an axiom, then your proof is fine. You just found another way to prove the same statement. Otherwise, there are structures that do not ...
1 vote

It seems that you have doubts concerning the text marked in yellow. Bourbaki is correct, but perhaps his wording is not perfect. So let us reformulate the axioms. (O$_I$) says that for each subset $\... • 4,604 1 vote Accepted ### Am I incorrectly interpreting axiom I, 3 of Hilbert's Foundations of Geometry? Claim: For every pair of points$A, B$there exists a point$C$not on$AB$. Proof: Suppose there does not exist any such point$C$. Then all points lie on$AB$. Then there is no set of three points ... • 1,860 1 vote ### Is dependent choice what one must use in this step of Artin's construction of the algebraic closure? This is not an answer to the question you asked, but three comments: First, note that in the construction of$K_1$alone you already need the axiom of choice just to choose the maximal ideal$m\$. ...
• 431k

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