How Long to Read Incompleteness in the Land of Sets

How Long Does it Take to Read Incompleteness in the Land of Sets?

It takes the average reader to read Incompleteness in the Land of Sets by Melvin Fitting

Assuming a reading speed of 250 words per minute. Learn more

Description

Russell's paradox arises when we consider those sets that do not belong to themselves. The collection of such sets cannot constitute a set. Step back a bit. Logical formulas define sets (in a standard model). Formulas, being mathematical objects, can be thought of as sets themselves-mathematics reduces to set theory. Consider those formulas that do not belong to the set they define. The collection of such formulas is not definable by a formula, by the same argument that Russell used. This quickly gives Tarski's result on the undefinability of truth. Variations on the same idea yield the famous results of Gödel, Church, Rosser, and Post. This book gives a full presentation of the basic incompleteness and undecidability theorems of mathematical logic in the framework of set theory. Corresponding results for arithmetic follow easily, and are also given. Gödel numbering is generally avoided, except when an explicit connection is made between set theory and arithmetic. The book assumes little technical background from the reader. One needs mathematical ability, a general familiarity with formal logic, and an understanding of the completeness theorem, though not its proof. All else is developed and formally proved, from Tarski's Theorem to Gödel's Second Incompleteness Theorem. Exercises are scattered throughout.

How long is Incompleteness in the Land of Sets?

Incompleteness in the Land of Sets by Melvin Fitting is 0 pages long, and a total of 0 words.

This makes it 0% the length of the average book. It also has 0% more words than the average book.

How Long Does it Take to Read Incompleteness in the Land of Sets Aloud?

The average oral reading speed is 183 words per minute. This means it takes to read Incompleteness in the Land of Sets aloud.

What Reading Level is Incompleteness in the Land of Sets?

Incompleteness in the Land of Sets is suitable for students ages 2 and up.

Note that there may be other factors that effect this rating besides length that are not factored in on this page. This may include things like complex language or sensitive topics not suitable for students of certain ages.

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