# Tagged Questions

In the philosophy of mathematics, intuitionism, or neointuitionism (opposed to preintuitionism), is an approach where mathematics is considered to be purely the result of the constructive mental activity of humans. That is, given a set of axioms, the only propositions that can exist are those that ...

27 views

### Algorithm to force decidability of statements using an intuitionistic series of new axioms

Consider pairs $(\Phi,n)$ where $\Phi$ is a finite set of statements in Peano arithmetic and $n$ is an integer. Say that $p'=(\Phi',n')$ is an elementary intuitionistic extension of $p=(\Phi,n)$ iff ...
93 views

### Proving the non-derivability of formula using the of the kripke model

I try proving the non-derivability of $(p\to q) \to \lnot p \lor q$, using the of the kripke model. I tried using different combinations of $Wi$, but I get fail.
53 views

### Why do you only need to show validity in one world when using trees in institutionist/constructivist logic?

Depicted below, my prof used a tree to prove that an argument is valid according to intuitionist logic. However, I can't find a contradiction in world 0. Why is invalidity ascertained when all ...
80 views

### Seeking help to understand a simple Kripke model

I'm reading A Brief Introduction to the Intuitionistic Propositional Calculus, at page 7, there is a simple Kripke model represented by a graph, I interpret it as: $W = \{w_1, w_2\}$ $w_1 \ge w_2$ ...
47 views

### Existence of a basis in constructive vector spaces

As I was trying to review forgotten knowledge on Vector Spaces in wikipedia, I read that the existence of a basis follows from Zorn lemma, hence equivalently from the axiom of choice. Actually, the ...
138 views

### Equivalence between Peirce's law and Excluded Middle in Intuitionistic logic

I'm searching for a intuitionistically valid proof of the formula : $[((P→Q)→P)→P] ↔ (P \lor \lnot P)$ using the "standard" Hilbert-style axiom system from Kleene [1952], for ...
82 views

### Is intuitionistic naive set theory consistent?

I'm asking because the usual argument that a set either belongs in itself or not doesn't apply. I did a quick search and it appears that the logic is also required to be contraction free. If it's ...