Everything about Heyting arithmetic

🧭 Start here: a 6-step reading path

1. Read the overview: Heyting arithmeticA 5-minute orientation
2. Skim a recent paper: Strictly Positive Fragments of the Provability Logic of Heyting ArithmeticInfluential work since 2022
3. Pick up a classic book: Sentences undecidable in formalized arithmeticThe most-reprinted book on the subject
4. Read the landmark paper: Uniform Heyting arithmeticCited 21 times
5. Go sideways: Church's thesis (constructive mathematics)A closely related topic
6. Go sideways: Constructive analysisA closely related topic

🏆 Landmark papers (most cited)

• Uniform Heyting arithmetic

  Ulrich Berger · 2005 · Annals of Pure and Applied Logic · 21 citations

• Fragments of Heyting arithmetic

  Wolfgang Burr · 2000 · Journal of Symbolic Logic · 20 citations

• Minimal models of Heyting arithmetic

  Ieke Moerdijk, Erik Palmgren · 1997 · Journal of Symbolic Logic · 17 citations

• Interactive Learning-Based Realizability for Heyting Arithmetic with EM1

  Federico Aschieri, Stefano Berardi · 2010 · Logical Methods in Computer Science · 14 citations

• On the structure of kripke models of heyting arithmetic

  Zoran Marković · 1993 · Mathematical Logic Quarterly · 10 citations

• Consistency of Heyting arithmetic in natural deduction

  Annika Kanckos · 2010 · Mathematical Logic Quarterly · 8 citations

• A parametrised functional interpretation of Heyting arithmetic

  Bruno Dinis, Paulo Oliva · 2021 · Annals of Pure and Applied Logic · 2 citations

• Interactive Realizability for second-order Heyting arithmetic with EM1 and SK1

  FEDERICO ASCHIERI · 2013 · Mathematical Structures in Computer Science · 1 citations

🆕 Influential since 2022

• Strictly Positive Fragments of the Provability Logic of Heyting Arithmetic

  Ana de Almeida Borges, Joost J. Joosten · 2024 · Studia Logica · 0 citations

• Intuitionistic sets and numbers: small set theory and Heyting arithmetic

  Stewart Shapiro, Charles McCarty, Michael Rathjen · 2024 · Archive for Mathematical Logic · 0 citations

📚 Books worth reading

• Sentences undecidable in formalized arithmeticAndrzej Mostowski · 1952
• 📕IntuitionismArend Heyting · 1956
• IntuitionismA. Heyting · 1956
• 📕Essays on the foundations of mathematicsUniversiṭah ha-ʻIvrit bi-Yerushalayim. · 1966

Ranked by number of editions on Open Library, a rough measure of how lasting a book is.

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