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Within 30 days after collecting your permit in the country, you must submit a document confirming your health insurance in Slovakia and prove that you do not suffer from a disease that constitutes a threat to public health.
You can file an administrative appeal to the Directorate of Alien Police/Directorate of Border and Alien Police.
You can file a judicial appeal to the Regional court.
More on visas
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More on working in Slovakia
More on coming to Slovakia as a researcher
Overview of all necessary information (including research and development)