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5644 results in Programming Languages and Applied Logic

Page 4 of 283

Programming in Ada 2022
  • John Barnes
  • Published online:
    21 November 2024
    Print publication:
    28 November 2024
  • The latest version of 'Programming in Ada' covers the full details of the core language Ada 2022 as approved by ISO in 2023, including new features that aid program proof and the efficient use of multicore architectures. The book is arranged in four parts. The first part introduces the key ideas to the newcomer with a working example illustrating the basic ideas. The algorithmic features, structural features such as OOP and multitasking, and details of the standard library and interaction with the external environment are all covered in subsequent parts. This comprehensive guide includes several working examples and is enhanced by a range of supplementary online materials, including a dozen complete executable programs, five of which illustrate important new features. 'Programming in Ada' is a must-have for anyone looking to learn Ada programming language, and will serve as a definitive reference for years to come.

  • Chapter 8 - Models of LSA as derived models

  • Grigor Sargsyan, Polish Academy of Sciences, Nam Trang, University of North Texas
  • Book:
    The Largest Suslin Axiom
    Published online:
    07 June 2024
    Print publication:
    27 June 2024, pp 213-234

  • Summary

    In this chapter, we show that under AD^+, the derived model of certain hod pairs satisfies the LSA. We also prove results that are important elsewhere. In particular, we show the derived model of an active \omega.2 lsa Woodin mouse satisfies LSA. This result will be important in Chapter 12, where we obtain the consistency of LSA from PFA.

  • Chapter 11 - A proof of square in LSA-small HOD mice

  • Grigor Sargsyan, Polish Academy of Sciences, Nam Trang, University of North Texas
  • Book:
    The Largest Suslin Axiom
    Published online:
    07 June 2024
    Print publication:
    27 June 2024, pp 309-334

  • Summary

    This chapter presents a proof $\square_{\kappa,2}$ holds in a lsa-small hod mouse $\mathcal{P}$ for all cardinals $\kappa$ of $\mathcal{P}$. The proof adapts a well-known construction of $\square$ in extender models by Schimmerling-Zeman. The main challenge to overcome in this situation is that the full condensation lemma, which holds for extender models, does not hold in hod mice. The main application of this result is in the proof of consistency of LSA in Chapter 12.

  • Chapter 9 - Condensing sets

  • Grigor Sargsyan, Polish Academy of Sciences, Nam Trang, University of North Texas
  • Book:
    The Largest Suslin Axiom
    Published online:
    07 June 2024
    Print publication:
    27 June 2024, pp 235-272

  • Summary

    This chapter develops the theory of condensing sets. Condensing sets give rise to iteration strategies with nice condensation properties. We show the existence of condensing sets under various hypotheses: AD^+ and PFA. We will use the existence of condensing sets in AD^+ in the proof of generation of pointclasses in Chapter 10. We will use the existence of condensing sets in Chapter 12 to construct a model of LSA under PFA.

Page 4 of 283