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4 votes
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 ...
Noah Schweber's user avatar
2 votes

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' ...
Bram28's user avatar
  • 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 ...
Hyperbolic Cake's user avatar
1 vote

Bourbaki General Topology: topological structure definition mistake

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 $\...
Kritiker der Elche's user avatar
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 ...
Numeral's user avatar
  • 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 $m$. ...
Qiaochu Yuan's user avatar

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