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Everything about Second-order arithmetic
Mathematical system
In mathematical logic, second-order arithmetic is a collection of axiomatic systems that formalize the natural numbers and their subsets. It is an alternative to axiomatic set theory as a foundation for much, but not all, of mathematics. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Second-order arithmeticA 5-minute orientation
- Skim a recent paper: Jensen Δn1 Reals by Means of ZFC and Second-Order Peano ArithmeticInfluential work since 2022
- Pick up a classic book: Standard and Non-standard Analysis in Second Order ArithmeticThe most-reprinted book on the subject
- Read the landmark paper: Weak Second‐Order Arithmetic and Finite AutomataCited 785 times
- Go sideways: Reverse mathematicsA closely related topic
- Go sideways: Ordinal analysisA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Weak Second‐Order Arithmetic and Finite Automata
Second order arithmetic and related topics
The limits of determinacy in second-order arithmetic
Uniform versions of some axioms of second order arithmetic
Formalizing forcing arguments in subsystems of second-order arithmetic
Fixed point theory in weak second-order arithmetic
Representability in some systems of second order arithmetic
Exponentiation and second-order bounded arithmetic
🆕 Influential since 2022
Jensen Δn1 Reals by Means of ZFC and Second-Order Peano Arithmetic
Parameterfree Comprehension Does Not Imply Full Comprehension in Second Order Peano Arithmetic
Second order arithmetic as the model companion of set theory
A NOTE ON FRAGMENTS OF UNIFORM REFLECTION IN SECOND ORDER ARITHMETIC
Notes on the Equiconsistency of ZFC Without the Power Set Axiom and Second-Order Arithmetic
📚 Books worth reading
- 📕Standard and Non-standard Analysis in Second Order ArithmeticKeita Yokoyama · 2009
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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