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vmcai - of Philipp Ruemmer
vmcai - of Philipp Ruemmer

brouwer`s intuitionism as a self-interpreted mathematical theory
brouwer`s intuitionism as a self-interpreted mathematical theory

071 Embeddings
071 Embeddings

... it stands because this disjunction gives the 0 of the lattice. We must treat each member of the list ...
an application of group theory to the analysis of
an application of group theory to the analysis of

Comparing sizes of sets
Comparing sizes of sets

DISCRETE MATHEMATICAL STRUCTURES
DISCRETE MATHEMATICAL STRUCTURES

... UNIT – 1 ...
SORT LOGIC AND FOUNDATIONS OF MATHEMATICS 1
SORT LOGIC AND FOUNDATIONS OF MATHEMATICS 1

... Sort logic, introduced in [7], is a many-sorted extension of second order logic. In an exact sense it is the strongest logic that there is. In this paper sort logic is suggested as a foundation of mathematics and contrasted to second order logic and to set theory. It is argued that sort logic solves ...
pdf
pdf

Strong Logics of First and Second Order
Strong Logics of First and Second Order

The 12th Delfino Problem and universally Baire sets of reals
The 12th Delfino Problem and universally Baire sets of reals

Introduction to Mathematical Logic lecture notes
Introduction to Mathematical Logic lecture notes

... we will be able to deduce (or “prove”) formulae from other formulae. Indeed, in real-life Mathematics, a proof is merely a sequence of assertions (alas, in an informal natural ...
Back to Basics: Revisiting the Incompleteness
Back to Basics: Revisiting the Incompleteness

page 139 MINIMIZING AMBIGUITY AND
page 139 MINIMIZING AMBIGUITY AND

Binary aggregation with integrity constraints Grandi, U. - UvA-DARE
Binary aggregation with integrity constraints Grandi, U. - UvA-DARE

Peano`s Arithmetic
Peano`s Arithmetic

... back to the publisher with corrections and his own suggestions for improvement. He even asked for permission to publish Genocchi’s lectures. After fixing some errors and adding his own comments to the collection, he only listed himself as an editor [2]. In 1884 Peano became a professor at the univer ...
Hybrid Interactive Theorem Proving using Nuprl and HOL?
Hybrid Interactive Theorem Proving using Nuprl and HOL?

Notes on Discrete Mathematics
Notes on Discrete Mathematics

Lecture 2
Lecture 2

Logic and Discrete Mathematics for Computer Scientists
Logic and Discrete Mathematics for Computer Scientists

Barwise: Infinitary Logic and Admissible Sets
Barwise: Infinitary Logic and Admissible Sets

Computer Science Foundation Exam
Computer Science Foundation Exam

Notes on Discrete Mathematics CS 202: Fall 2013 James Aspnes 2014-10-24 21:23
Notes on Discrete Mathematics CS 202: Fall 2013 James Aspnes 2014-10-24 21:23

Natural Numbers and Natural Cardinals as Abstract Objects
Natural Numbers and Natural Cardinals as Abstract Objects

Circuit principles and weak pigeonhole variants
Circuit principles and weak pigeonhole variants

< 1 2 3 4 5 6 7 8 ... 37 >

Naive set theory

Naive set theory is one of several theories of sets used in the discussion of the foundations of mathematics. Unlike axiomatic set theories, which are defined using a formal logic, naive set theory is defined informally, in natural language. It describes the aspects of mathematical sets familiar in discrete mathematics (for example Venn diagrams and symbolic reasoning about their Boolean algebra), and suffices for the everyday usage of set theory concepts in contemporary mathematics.Sets are of great importance in mathematics; in fact, in modern formal treatments, most mathematical objects (numbers, relations, functions, etc.) are defined in terms of sets. Naive set theory can be seen as a stepping-stone to more formal treatments, and suffices for many purposes.
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