# Tag Info

### Can you give me an example of an implicit use of Godel's Completeness Theorem, say for example in group theory?

A simple example might be something like the following: Proposition: An element $g \in G$ of a group and any of its conjugates $hgh^{-1} \in G$ have the same order. This is a collection of first-...
• 442k
Accepted

### The meaning of an implication with the existential quantifier

Example c was written: $\exists x (C(x) \to F(x))$ The answer to that example was given as "Someone is a comedian and that means they are funny" That is an incorrect translation. Imagine a ...
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### The meaning of an implication with the existential quantifier

"Someone is a comedian and that means they are funny" actually means $$\exists x\, C(x)\land \forall x\,\big(C(x)\to F(x)\big),$$ which is a logically stronger assertion than ∃x\,\big(C(x) ...
• 40.7k
Accepted

### A first order theory of $\mathbb{R}$

The first-order theory of $\mathbb{R}$ is well-understood. It is one of the oldest and most important examples in the field of model theory. An ordered field $R$ is real closed if every positive ...
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### Can you give me an example of an implicit use of Godel's Completeness Theorem, say for example in group theory?

It's worth noting that we rarely care about the existence of a first-order proof from a given set of axioms. A first-order proof is a very messy object, and if we're not already interested in them for ...
• 252k
Accepted

### Hilbert style proof systems vs Natural deductions: Some naive questions

A: The first thing to note is that the 'hypotheses' that the website talks about are not the statements in $\Gamma$. The statements in $\Gamma$ are often referred to as premises. Both natural ...
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