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Results tagged with intuitionism
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user 101577
0
votes
How strong is Cantor-Bernstein-Schröder?
The Cantor-Schröder-Bernstein theorem (CBS) implies excluded middle in intuitionistic mathematics (INT) and in recursive mathematics (RUSS), since CBS is false ($\neg$CBS is a theorem), and ex falso q …
- 1,616
1
vote
Accepted
Fixed-point property and $T_0$ separation property
Consider in intuitionistic mathematics the example of $A$ being the unit interval $[0,1]$ with the trivial topology $\{\emptyset,[0,1]\}$.
Then $A$ is not $T_0$ and yet $A$ still has the fixed-point …
- 1,616
2
votes
Adding nonconstructive disjunction to intuitionistic logic
${\rm\small\color{#808080}{(1st\ answer, also\ see\ updates\ below):}}$
I think the connective $A⅋B$ is not more constructive than existing connectives. You say that a witness for$A⅋B$ consists of two …
- 1,616
4
votes
Accepted
Why is the notion of algorithm a primitive one in Brouwer's intuitionism?
Since the work of Church and Turing (say around 1936), the notion of algorithm is definitely not considered primitive in intuitionism. …
- 1,616
1
vote
Admissibility of Harrop's rule, computationally
The way I understand it is as follows. The most general formula
$
(\neg A \; \to \; B \vee C) \;\; \to \;\;
((\neg A \; \to \; B) \vee (\neg A \; \to \; C))
$
is not derivable in IPC, because it …
- 1,616