@article{turing1936computable, title={On computable numbers, with an application to the Entscheidungsproblem}, author={Turing, Alan Mathison and others}, journal={J. of Math}, volume={58}, number={345-363}, pages={5}, year={1936}, publisher={Wiley Online Library} } @article{hanf1975boolean, title={The Boolean algebra of logic}, author={Hanf, William}, journal={Bulletin of the American Mathematical Society}, volume={81}, number={3}, pages={587--589}, year={1975} } @article{soare2016turing, title={Turing computability: theory and applications}, author={Soare, Robert I}, journal={Theory Appl. Comput}, year={2016}, publisher={Springer} } @article{simpson1977first, title={First-order theory of the degrees of recursive unsolvability}, author={Simpson, Stephen G}, journal={Annals of Mathematics}, volume={105}, number={1}, pages={121--139}, year={1977}, publisher={JSTOR} } @book{simpson2009subsystems, title={Subsystems of second order arithmetic}, author={Simpson, Stephen George}, volume={1}, year={2009}, publisher={Cambridge University Press} } @book{stillwell2018reverse, title={Reverse mathematics: Proofs from the inside out}, author={Stillwell, John}, year={2018}, publisher={Princeton University Press} } @book{downey2010algorithmic, title={Algorithmic randomness and complexity}, author={Downey, Rodney G and Hirschfeldt, Denis R}, year={2010}, publisher={Springer Science \& Business Media} } @book{rautenberg2006concise, title={A concise introduction to mathematical logic}, author={Rautenberg, Wolfgang}, year={2006}, publisher={Springer} } @book{cutland1980computability, title={Computability: An introduction to recursive function theory}, author={Cutland, Nigel}, year={1980}, publisher={Cambridge university press} } @article{post1944recursively, title={Recursively enumerable sets of positive integers and their decision problems}, author={Post, Emil L}, journal={Bull. Amer. Math. Soc.}, volume={50}, pages={284--316}, year={1944} } @book{cooper2017computability, title={Computability theory}, author={Cooper, S Barry}, year={2017}, publisher={Chapman and Hall/CRC} }