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Everything about Robinson arithmetic
Axiomatic logical system
In mathematics, Robinson arithmetic is a finitely axiomatized fragment of first-order Peano arithmetic (PA), first set out by Raphael M. Robinson in 1950. It is usually denoted Q. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Robinson arithmeticA 5-minute orientation
- Pick up a classic book: Introduction to The National Arithmetic, on the Inductive SystemThe most-reprinted book on the subject
- Read the landmark paper: MUTUAL INTERPRETABILITY OF ROBINSON ARITHMETIC AND ADJUNCTIVE SET THEORY WITH EXTENSIONALITYCited 9 times
- Go sideways: General set theoryA closely related topic
- Go sideways: Peano axiomsA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
MUTUAL INTERPRETABILITY OF ROBINSON ARITHMETIC AND ADJUNCTIVE SET THEORY WITH EXTENSIONALITY
Interpretability of Robinson arithmetic in the ramified second-order theory of dense linear order.
The Professional Education of Elementary Teachers in the Field of Arithmetic. Arthur E. Robinson
Julia Robinson. Existential definability in arithmetic. Transactions of the American Mathematical Society, Bd. 72 (1952), S. 437–449.
📚 Books worth reading
Introduction to The National Arithmetic, on the Inductive SystemBenjamin Greenleaf · 1844
The progressive higher arithmeticHoratio N. Robinson · 1867
The Progressive Higher ArithmeticDaniel W. Fish, Horatio N. Robinson · 1866
Robinson's Progressive Intellectual Arithmetic: On the Inductive Plan. Being a Sequel to the ..Horatio N. Robinson · 1863
The progressive practical arithmeticHoratio N. Robinson · 1860- 📕Robinson's progressive primary arithmeticHoratio N. Robinson, Daniel W. Fish · 1876
Key to the Progressive practical arithmeticHoratio N. Robinson · 1860
Robinson's progressive primary arithmeticHoratio N. Robinson · 1863
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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- Gödel's incompleteness theorems Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories.…
- Gentzen's consistency proof Gentzen's consistency proof is a result of proof theory in mathematical logic, published by Gerhard Gentzen in 1936. It shows that the Peano axioms of…
- Ω-consistent theory In mathematical logic, an ω-consistent (or omega-consistent, or numerically segregative) theory is a theory (collection of sentences) that is not only…
- Satisfiability In mathematical logic, a formula is satisfiable if it is true under some assignment of values to its variables. For example, the formula x + 3 = y {\displaystyl…
- Undecidable problem In computability theory and computational complexity theory, an undecidable problem is a decision problem for which it is proved to be impossible to construct…
- Self-verifying theories Self-verifying theories are consistent first-order systems of arithmetic, much weaker than Peano arithmetic, that are capable of proving their own consistency…