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not always A \models \phi or A \models \neg \phi example
https://math.stackexchange.com/q/2344917
Consider the structure \mathbb N of natural numbers and consider the formula (x=0). For a valuation v such that v(x)=0 we have: \mathbb N, v \vDash (x=0) while obviously, for a valuation ...
Equivalence to a universal formula
https://math.stackexchange.com/questions/195216/equivalence-to-a-universal-formula
Here are a couple of hints: (1) Prove this first for sentences \chi instead of formulas. (2) When working with sentences, do not explicitly construct the universal sentence \chi^*. Instead, ...
Express Integer as Sum of Two Squares
https://math.stackexchange.com/questions/366421/express-integer-as-sum-of-two-squares
I'm not an expert, but from memory something which it turns out is called the Brahmagupta–Fibonacci identity or occasionally Diophantus identity (used constructively in the proof of the result of ...
For types, is being definable is strictly stronger than being isolated?
https://math.stackexchange.com/questions/610357/for-types-is-being-definable-is-strictly-stronger-than-being-isolated
This is strictly stronger. Let T be a theory asserting that c_n are infinitely many distinct constants. The type of an element which is distinct then all these constants is not isolated (it is ...
Question about Logical implication
https://math.stackexchange.com/questions/482536/question-about-logical-implication/483217
Suppose A = \varnothing. Then, for any truth value assignment w, w(\psi) = 1 (vacuously) for each and every \psi \in A = \varnothing Why? Because there are no \psi \in A = \varnothing ...
Countable dimensional normed space incomplete
https://math.stackexchange.com/q/2824460
Now that you know BCT and the fact that all finite dimensional normed vector spaces are Euclidean, the proof is very straight-forward. As you argued, there is some n\in\mathbb N such that \operatorname{int}C_n\ne\emptyset ...
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