Logic in Computer Science - Liacs
Logic in Computer Science - Liacs
Logic in Computer Science - Liacs
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The Russell paradox<br />
Cantor set theory is <strong>in</strong>consistent (1901)<br />
If T = { x | x ∉ x } then x ∈ x ⇔ x ∉ x<br />
Russel and Whitehead Pr<strong>in</strong>cipia Mathematica (1919):<br />
Solution by us<strong>in</strong>g a hierarchy of sets (type theory)<br />
Sets of a given type can conta<strong>in</strong> sets of preced<strong>in</strong>g types (those<br />
lower <strong>in</strong> the hierarchy), thus prevent<strong>in</strong>g loops.<br />
Zermelo-Fraenkel axiomatic set theory (1922)<br />
Set theory as foundation of mathematics<br />
<strong>Logic</strong> a - Spr<strong>in</strong>g 2011<br />
Slide 14<br />
1/22/2013<br />
14
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