About to read: Inexhaustibility: A Non-Exhaustive Treatment, 2017

About to read:
Inexhaustibility: A Non-Exhaustive Treatment, 2017
It’s about the _positive_ side of incompleteness; the amount of factual possibilities available simply cannot be exhausted; just as many as you find, there will always be more combinations, more ways, more uniqueness,
It may be interesting or may be dry. I’m just glad for the places online available for me to find these kinds of things.
” sustained presentation of a particular view of the topic of Gödelian extensions of theories. It presents the basic material in predicate logic, set theory and recursion theory, leading to a proof of Gödel’s incompleteness theorems. The inexhaustibility of mathematics is treated based on the concept of transfinite progressions of theories as conceived by Turing and Feferman.”
1 Introduction
2 Arithmetical preliminaries
3 Primes and proofs
4 The language of arithmetic
5 The language of analysis
6 Ordinals and inductive definitions
7 Formal languages and the definition of truth
8 Logic and theories
9 Peano Arithmetic and computability
10 Elementary and classical analysis
11 The recursion theorem and ordinal notations
12 The incompleteness theorems
13 Iterated consistency
14 Iterated reflection
15 Iterated iteration and inexhaustibility

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