15.541 logic questions.

Symbol for null proposition in mathematical logic

Is there a symbol in mathematical logic expressing a null statement? That is an equivalent expression to: $$p\land\lnot p$$

1 Countable normal interpretations of $(=, <)$ elementary equivalent but not isomorphic to $\mathbb{Q}$ and $\mathbb{Q}^+$

0 answers, 14 views logic first-order-logic
Are there any normal interpretations of $(=, <)$ with countable domain that are elementary equivalent but not isomorphic to $\mathbb{Q}$? To $\mathbb{Q}^+ = \mathbb{Q} \cap [0; +\infty)$? First, I ...

-1 This translate in the logic predicate is true or not

I found in a book , this phrase :There is a man who loves all women. the logic predicate is : $\exists x(m(x)\wedge\forall y(w(y)\wedge love(x,y)))$ or not

Translate each of the following sentences into symbolic logic

0 answers, 82 views logic self-learning logic-translation
I would like someone to give me some advice on whether I did these right or not. Here are the two sentences: For every positive number K there is a positive number M for which |f (x)-b| < K, ...

1 Order of Two Operators

Let's start by looking at the following example from ring theory: Let $A$ and $B$ be commutative rings with identity and let $f:A\to B$ be a ring homomorphism. For every ideal $I$ of $A$, the ...

3 “Predicate” vs. “Relation”

4 answers, 846 views logic soft-question terminology relations

Maximal (or prime) theories and their sets

Probably it is very simple lemma but I cannot see it. Suppose that we have intuitionistic propositional logic (in fact, it can be classical) and $W$ is the set of all prime (or maximal - in classical ...

3 Some questions about the proof of Godel's first incompleteness theorem

I have some questions about the commonly presented proof of Godel's first incompleteness theorem. First of all, what is the need for the Godel numbers in the proof? Would not the proof be valid ...

2 Distance from a convex set to a point

Let $Y \in \mathbb{R}^n$ be a nonempty convex set such that $0 \notin Y$ and fix $y_1,\dots,y_n$ in $Y$, where $n \ge 2$. I know that there exist $i,j$ such that $\Vert y_i \Vert > \Vert y_j\Vert$....

1 Approach validation: Model of the diagram of a structure has isomorphic submodel

1 answers, 22 views proof-verification logic model-theory
The problem: Let $N$ be an $L$-structure for a language $L$. The $diagram$ of $N$, $D(N)$ is the set of all quantifier-free $L_N$-sentences true in $N$. Suppose $M$ is a model of $D(N)$. Show that $M$...